Stochastic observability test for discrete-time kalman filters

Vibhor L. Bageshwar, Demoz Gebre-Egziabher, William L. Garrard, Tryphon T. Georgiou

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38 Scopus citations

Abstract

Stochastic observability refers to the existence of a filter for which the errors of the estimated state mean vector have bounded variance. In this paper, we derive a test to assess the stochastic observability of a Kalman filter implemented for discrete linear time-varying stochastic systems. This test is derived with the assumptions that the system matrices consist of known deterministic parameters and that there is complete uncertainty in the statistics of the initial state vector. This test can also be used to assess the stochastic observability of extended Kalman filters implemented for nonlinear stochastic systems linearized about the true state vector trajectory. We illustrate the utility of the stochastic observability test using an aided inertial navigation system.Wealso provide a counterexample to illustrate that observability is a necessary, but not sufficient, condition for the stochastic observability of a Kalman filter implemented for a system.

Original languageEnglish (US)
Pages (from-to)1356-1370
Number of pages15
JournalJournal of Guidance, Control, and Dynamics
Volume32
Issue number4
DOIs
StatePublished - 2009

Bibliographical note

Funding Information:
This work was partially supported by NASA under Minnesota Space Grant NNG05GG39H.

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